We use Galaxy Zoo 2 visual classifications to study the morphological signatures of interaction between similar-mass galaxy pairs in the Sloan Digital Sky Survey. We find that many observable features correlate with projected pair separation - not only obvious indicators of merging, disturbance and tidal tails, but also more regular features, such as spiral arms and bars. These trends are robustly quantified, using a control sample to account for observational biases, producing measurements of the strength and separation scale of various morphological responses to pair interaction. For example, we find that the presence of spiral features is enhanced at scales less than or similar to 70 h(70)(-1) kpc, probably due to both increased star formation and the formation of tidal tails. On the other hand, the likelihood of identifying a bar decreases significantly in pairs with separations less than or similar to 30 h(70)(-1) kpc, suggesting that bars are suppressed by close interactions between galaxies of similar mass. We go on to show how morphological indicators of physical interactions provide a way of significantly refining standard estimates for the frequency of close pair interactions, based on velocity offset and projected separation. The presence of loosely wound spiral arms is found to be a particularly reliable signal of an interaction, for projected pair separations up to similar to 100 h(70)(-1) kpc. We use this indicator to demonstrate our method, constraining the fraction of low-redshift galaxies in truly interacting pairs, with M-* > 10(9.5) M-circle dot and mass ratio <4, to be between 0.4 and 2.7 per cent.